Linear transform for simultaneous diagonalization of covariance and perceptual metric matrix in image coding

Two types of redundancies are contained in images: statistical redundancy and psychovisual redundancy. Image representation techniques for image coding should remove both redundancies in order to obtain good results. In order to establish an appropriate representation, the standard approach to transform coding only considers the statistical redundancy, whereas the psychovisual factors are introduced after the selection of the representation as a simple scalar weighting in the transform domain.In this work, we take into account the psychovisual factors in the definition of the representation together with the statistical factors, by means of the perceptual metric and the covariance matrix, respectively. In general the ellipsoids described by these matrices are not aligned. Therefore, the optimal basis for image representation should simultaneously diagonalize both matrices. This approach to the basis selection problem has several advantages in the particular application of image coding. As the transform domain is Euclidean (by definition), the quantizer design is highly simplified and at the same time, the use of scalar quantizers is truly justified. The proposed representation is compared to covariance-based representations such as the DCT and the KLT or PCA using standard JPEG-like and Max-Lloyd quantizers.